Consider the following figure. (a) A conducting loop in the shape of a square of

Question

Consider the following figure. (a) A conducting loop in the shape of a square of edge length I = 0.440 m carries a current I = 9.80 A as in the figure above. Calculate the magnitude and direction of the magnetic field at the center of the square. magnitude What is the contribution to the field of a single edge of the square loop? mu T direction (b) If this conductor is reshaped to form a circular loop and carries the same current, what is the value of the magnetic field at the center? magnitude mu T direction

Explanation / Answer

Here, each side produces a field into the page

all the four sides produce

B = 4 * Mu0*I/4*pi*a * [ sin 45 - sin (-45)] where a = l/2

B = 2*sqqt2 * Mu0 *I /( pi*l)

B= 2*1.414*4*10^-7*9.8 / 0.44 = 25.1*10^-6 Tesla into the PAGE

b)

Fo a single circular turn, we have 4*l = 2*pi*R

B = Mu0*pi*I/4*l = 4*pi*10^-7*3.14*9.8/4*0.44 = 21.96*10^-6 Tesla into the Page

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